5  Appendix B

5.1 Setup

5.1.1 Install Packages

We install the following packages using the groundhog package manager to increase computational reproducibility.

options(repos = c(CRAN = "https://cran.r-project.org")) 

if (!requireNamespace("groundhog", quietly = TRUE)) {
    install.packages("groundhog")
}

pkgs <- c("magrittr", "data.table", "stringr", "Rmisc", "ggplot2",
          "lmtest", "sandwich", "stargazer")

groundhog::groundhog.library(pkg = pkgs,
                             date = "2024-08-01")

rm(pkgs)

5.1.2 Read Data

data      <- readRDS(file="../data/processed/full.Rda")
timeSpent <- data.table::fread(file = "../data/raw/PageTimes-2021-09-15.csv")
raw       <- data.table::fread(file="../data/raw/all_apps_wide_2021-09-15.csv")

5.2 Table B.1

::: {#tbl-B-1 .cell tbl-cap=’ ’}

ols_1 <- lm(formula = E1 ~ surprise + treated + surprise * treated,
              data = data)
  se_1  <- coeftest(x = ols_1, 
                    vcov = vcovCL(ols_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))
  
  ols_2 <- lm(formula = E1 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == FALSE))
  se_2  <- coeftest(x = ols_2, 
                    vcov = vcovCL(ols_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))
  
  ols_3 <- lm(formula = E1 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == TRUE))
  se_3  <- coeftest(x = ols_3, 
                    vcov = vcovCL(ols_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))
  
  ols_4 <- lm(formula = E1 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "point"))
  se_4  <- coeftest(x = ols_4, 
                    vcov = vcovCL(ols_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))
  
  ols_5 <- lm(formula = E1 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "interval"))
  se_5  <- coeftest(x = ols_5, 
                    vcov = vcovCL(ols_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))
  
  ols_6 <- lm(formula = E1 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "both"))
  se_6  <- coeftest(x = ols_6, 
                    vcov = vcovCL(ols_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))
  
  
  
  se <- list(se_1[,2], se_2[,2], se_3[,2], se_4[,2], se_5[,2], se_6[,2])
  p  <- list(se_1[,4], se_2[,4], se_3[,4], se_4[,4], se_5[,4], se_6[,4])
  
  stargazer(ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, 
            align = TRUE, 
            se = se, 
            p = p,   
            title = "Linear regressions: Treatment effects on E1",
            dep.var.caption = "Dependent variable: E1",
            dep.var.labels = " ",
            model.names = FALSE,
            column.labels = c("full", "confirmation", "contradiction", "point", "interval", "both"),
            covariate.labels = c("contradiction", "both", "interval", "stage 2", "contradiction x stage 2", "both x stage 2", "interval x stage 2", "Constant"),
            font.size = "scriptsize",
            type = "html", 
            df = FALSE,
          notes = c("The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)"),
          notes.align = "l")
Linear regressions: Treatment effects on E1
Dependent variable: E1
full confirmation contradiction point interval both
(1) (2) (3) (4) (5) (6)
contradiction -0.962 -1.492 0.951 -2.435
(1.080) (1.760) (1.993) (1.855)
both 2.430 1.487
(1.759) (1.856)
interval 1.331 3.773**
(1.836) (1.923)
stage 2 -1.036 0.955 7.468*** 0.955 -1.634 -2.504*
(0.846) (1.500) (1.791) (1.500) (1.498) (1.391)
contradiction x stage 2 7.563*** 6.513*** 4.269* 12.098***
(1.315) (2.336) (2.232) (2.251)
both x stage 2 -3.459* 2.126
(2.046) (2.517)
interval x stage 2 -2.589 -4.833**
(2.120) (2.437)
Constant 47.893*** 46.653*** 45.161*** 46.653*** 47.984*** 49.083***
(0.747) (1.193) (1.294) (1.193) (1.395) (1.293)
Observations 3,010 1,490 1,520 1,014 1,002 994
R2 0.014 0.002 0.024 0.015 0.006 0.028
Adjusted R2 0.013 -0.002 0.021 0.012 0.003 0.025
Residual Std. Error 23.210 22.727 23.652 22.494 23.624 23.473
F Statistic 13.967*** 0.530 7.531*** 5.226*** 2.152* 9.393***
Note: p<0.1; p<0.05; p<0.01
The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)

:::

5.3 Table B.2

::: {#tbl-B-2 .cell tbl-cap=’ ’}

ols_1 <- lm(formula = E2 ~ surprise + treated + surprise * treated,
              data = data)
  se_1  <- coeftest(x = ols_1, 
                    vcov = vcovCL(ols_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))
  
  ols_2 <- lm(formula = E2 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == FALSE))
  se_2  <- coeftest(x = ols_2, 
                    vcov = vcovCL(ols_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))
  
  ols_3 <- lm(formula = E2 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == TRUE))
  se_3  <- coeftest(x = ols_3, 
                    vcov = vcovCL(ols_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))
  
  ols_4 <- lm(formula = E2 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "point"))
  se_4  <- coeftest(x = ols_4, 
                    vcov = vcovCL(ols_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))
  
  ols_5 <- lm(formula = E2 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "interval"))
  se_5  <- coeftest(x = ols_5, 
                    vcov = vcovCL(ols_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))
  
  ols_6 <- lm(formula = E2 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "both"))
  se_6  <- coeftest(x = ols_6, 
                    vcov = vcovCL(ols_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))
  
  
  
  se <- list(se_1[,2], se_2[,2], se_3[,2], se_4[,2], se_5[,2], se_6[,2])
  p  <- list(se_1[,4], se_2[,4], se_3[,4], se_4[,4], se_5[,4], se_6[,4])
  
  stargazer(ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, 
            align = TRUE, 
            se = se, 
            p = p,   
            title = "Linear regressions: Treatment effects on E2",
            dep.var.caption = "Dependent variable: E2",
            dep.var.labels = " ",
            model.names = FALSE,
            column.labels = c("full", "confirmation", "contradiction", "point", "interval", "both"),
            covariate.labels = c("contradiction", "both", "interval", "stage 2", "contradiction x stage 2", "both x stage 2", "interval x stage 2", "Constant"),
            font.size = "scriptsize",
            type = "html", 
            df = FALSE,
          notes = c("The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)"),
          notes.align = "l")
Linear regressions: Treatment effects on E2
Dependent variable: E2
full confirmation contradiction point interval both
(1) (2) (3) (4) (5) (6)
contradiction -1.235 -1.497 -1.578 -0.612
(1.072) (1.779) (1.943) (1.852)
both 1.558 2.443
(1.806) (1.825)
interval 0.174 0.092
(1.867) (1.858)
stage 2 3.535*** 4.227*** -3.103** 4.227*** 2.998** 3.348**
(0.782) (1.159) (1.407) (1.159) (1.468) (1.433)
contradiction x stage 2 -5.636*** -7.331*** -3.812* -5.768***
(1.125) (1.824) (1.977) (2.059)
both x stage 2 -0.879 0.683
(1.843) (2.041)
interval x stage 2 -1.230 2.289
(1.871) (1.932)
Constant 50.681*** 50.108*** 48.611*** 50.108*** 50.282*** 51.666***
(0.757) (1.250) (1.265) (1.250) (1.387) (1.304)
Observations 3,010 1,490 1,520 1,014 1,002 994
R2 0.013 0.007 0.005 0.023 0.008 0.010
Adjusted R2 0.012 0.004 0.002 0.020 0.005 0.007
Residual Std. Error 21.997 22.066 21.941 20.890 22.813 22.276
F Statistic 12.879*** 2.214* 1.655 7.827*** 2.700** 3.462**
Note: p<0.1; p<0.05; p<0.01
The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)

:::

5.4 Table B.3

::: {#tbl-B-3 .cell tbl-cap=’ ’}

ols_1 <- lm(formula = E3 ~ surprise + treated + surprise * treated,
              data = data)
  se_1  <- coeftest(x = ols_1, 
                    vcov = vcovCL(ols_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))
  
  ols_2 <- lm(formula = E3 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == FALSE))
  se_2  <- coeftest(x = ols_2, 
                    vcov = vcovCL(ols_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))
  
  ols_3 <- lm(formula = E3 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == TRUE))
  se_3  <- coeftest(x = ols_3, 
                    vcov = vcovCL(ols_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))
  
  ols_4 <- lm(formula = E3 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "point"))
  se_4  <- coeftest(x = ols_4, 
                    vcov = vcovCL(ols_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))
  
  ols_5 <- lm(formula = E3 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "interval"))
  se_5  <- coeftest(x = ols_5, 
                    vcov = vcovCL(ols_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))
  
  ols_6 <- lm(formula = E3 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "both"))
  se_6  <- coeftest(x = ols_6, 
                    vcov = vcovCL(ols_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))
  
  
  
  se <- list(se_1[,2], se_2[,2], se_3[,2], se_4[,2], se_5[,2], se_6[,2])
  p  <- list(se_1[,4], se_2[,4], se_3[,4], se_4[,4], se_5[,4], se_6[,4])
  
  stargazer(ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, 
            align = TRUE, 
            se = se, 
            p = p,   
            title = "Linear regressions: Treatment effects on E3",
            dep.var.caption = "Dependent variable: E3",
            dep.var.labels = " ",
            model.names = FALSE,
            column.labels = c("full", "confirmation", "contradiction", "point", "interval", "both"),
            covariate.labels = c("contradiction", "both", "interval", "stage 2", "contradiction x stage 2", "both x stage 2", "interval x stage 2", "Constant"),
            font.size = "scriptsize",
            type = "html", 
            df = FALSE,
          notes = c("The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)"),
          notes.align = "l")
Linear regressions: Treatment effects on E3
Dependent variable: E3
full confirmation contradiction point interval both
(1) (2) (3) (4) (5) (6)
contradiction -0.317 1.231 0.356 -2.623
(1.049) (1.814) (1.864) (1.767)
both 4.813*** 0.958
(1.752) (1.828)
interval 2.199 1.323
(1.787) (1.889)
stage 2 0.148 2.161 -5.425*** 2.161 -0.006 -1.779
(0.818) (1.477) (1.635) (1.477) (1.283) (1.469)
contradiction x stage 2 -3.721*** -7.585*** -2.558 -0.971
(1.217) (2.204) (1.972) (2.136)
both x stage 2 -3.940* 2.675
(2.083) (2.253)
interval x stage 2 -2.167 2.861
(1.956) (2.217)
Constant 48.591*** 46.278*** 47.510*** 46.278*** 48.477*** 51.091***
(0.733) (1.204) (1.357) (1.204) (1.321) (1.274)
Observations 3,010 1,490 1,520 1,014 1,002 994
R2 0.006 0.004 0.009 0.012 0.002 0.007
Adjusted R2 0.005 0.001 0.006 0.009 -0.001 0.004
Residual Std. Error 22.475 21.461 23.399 22.160 22.847 22.373
F Statistic 5.563*** 1.320 2.815** 4.050*** 0.678 2.489*
Note: p<0.1; p<0.05; p<0.01
The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)

:::

5.5 Table B.4

::: {#tbl-B-4 .cell tbl-cap=’ ’}

ols_1 <- lm(formula = E12 ~ surprise + treated + surprise * treated,
              data = data)
  se_1  <- coeftest(x = ols_1, 
                    vcov = vcovCL(ols_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))
  
  ols_2 <- lm(formula = E12 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == FALSE))
  se_2  <- coeftest(x = ols_2, 
                    vcov = vcovCL(ols_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))
  
  ols_3 <- lm(formula = E12 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == TRUE))
  se_3  <- coeftest(x = ols_3, 
                    vcov = vcovCL(ols_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))
  
  ols_4 <- lm(formula = E12 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "point"))
  se_4  <- coeftest(x = ols_4, 
                    vcov = vcovCL(ols_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))
  
  ols_5 <- lm(formula = E12 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "interval"))
  se_5  <- coeftest(x = ols_5, 
                    vcov = vcovCL(ols_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))
  
  ols_6 <- lm(formula = E12 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "both"))
  se_6  <- coeftest(x = ols_6, 
                    vcov = vcovCL(ols_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))
  
  
  
  se <- list(se_1[,2], se_2[,2], se_3[,2], se_4[,2], se_5[,2], se_6[,2])
  p  <- list(se_1[,4], se_2[,4], se_3[,4], se_4[,4], se_5[,4], se_6[,4])
  
  stargazer(ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, 
            align = TRUE, 
            se = se, 
            p = p,   
            title = "Linear regressions: Treatment effects on E12",
            dep.var.caption = "Dependent variable: E12",
            dep.var.labels = " ",
            model.names = FALSE,
            column.labels = c("full", "confirmation", "contradiction", "point", "interval", "both"),
            covariate.labels = c("contradiction", "both", "interval", "stage 2", "contradiction x stage 2", "both x stage 2", "interval x stage 2", "Constant"),
            font.size = "scriptsize",
            type = "html", 
            df = FALSE,
          notes = c("The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)"),
          notes.align = "l")
Linear regressions: Treatment effects on E12
Dependent variable: E12
full confirmation contradiction point interval both
(1) (2) (3) (4) (5) (6)
contradiction -0.453 0.446 -1.087 -0.776
(1.031) (1.772) (1.754) (1.838)
both 1.672 0.451
(1.760) (1.850)
interval 2.072 0.539
(1.743) (1.783)
stage 2 1.817** 3.090** 4.460*** 3.090** -0.401 2.684*
(0.828) (1.365) (1.611) (1.365) (1.499) (1.440)
contradiction x stage 2 3.950*** 1.370 5.012** 5.592***
(1.198) (2.112) (2.050) (2.065)
both x stage 2 -0.406 3.816*
(1.984) (2.187)
interval x stage 2 -3.491* 0.150
(2.027) (2.134)
Constant 58.358*** 57.127*** 57.573*** 57.127*** 59.200*** 58.800***
(0.716) (1.230) (1.276) (1.230) (1.234) (1.258)
Observations 3,010 1,490 1,520 1,014 1,002 994
R2 0.010 0.004 0.019 0.008 0.007 0.021
Adjusted R2 0.009 0.001 0.015 0.005 0.004 0.018
Residual Std. Error 22.155 21.169 23.078 22.444 21.919 22.090
F Statistic 10.599*** 1.214 5.751*** 2.679** 2.266* 7.149***
Note: p<0.1; p<0.05; p<0.01
The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)

:::

5.6 Table B.5

::: {#tbl-B-5 .cell tbl-cap=’ ’}

ols_1 <- lm(formula = E13 ~ surprise + treated + surprise * treated,
              data = data)
  se_1  <- coeftest(x = ols_1, 
                    vcov = vcovCL(ols_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))
  
  ols_2 <- lm(formula = E13 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == FALSE))
  se_2  <- coeftest(x = ols_2, 
                    vcov = vcovCL(ols_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))
  
  ols_3 <- lm(formula = E13 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == TRUE))
  se_3  <- coeftest(x = ols_3, 
                    vcov = vcovCL(ols_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))
  
  ols_4 <- lm(formula = E13 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "point"))
  se_4  <- coeftest(x = ols_4, 
                    vcov = vcovCL(ols_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))
  
  ols_5 <- lm(formula = E13 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "interval"))
  se_5  <- coeftest(x = ols_5, 
                    vcov = vcovCL(ols_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))
  
  ols_6 <- lm(formula = E13 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "both"))
  se_6  <- coeftest(x = ols_6, 
                    vcov = vcovCL(ols_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))
  
  
  
  se <- list(se_1[,2], se_2[,2], se_3[,2], se_4[,2], se_5[,2], se_6[,2])
  p  <- list(se_1[,4], se_2[,4], se_3[,4], se_4[,4], se_5[,4], se_6[,4])
  
  stargazer(ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, 
            align = TRUE, 
            se = se, 
            p = p,   
            title = "Linear regressions: Treatment effects on E13",
            dep.var.caption = "Dependent variable: E13",
            dep.var.labels = " ",
            model.names = FALSE,
            column.labels = c("full", "confirmation", "contradiction", "point", "interval", "both"),
            covariate.labels = c("contradiction", "both", "interval", "stage 2", "contradiction x stage 2", "both x stage 2", "interval x stage 2", "Constant"),
            font.size = "scriptsize",
            type = "html", 
            df = FALSE,
          notes = c("The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)"),
          notes.align = "l")
Linear regressions: Treatment effects on E13
Dependent variable: E13
full confirmation contradiction point interval both
(1) (2) (3) (4) (5) (6)
contradiction 0.922 -2.686 4.258** 1.173
(1.037) (1.743) (1.846) (1.792)
both 0.479 4.338**
(1.749) (1.786)
interval -1.358 5.586***
(1.811) (1.779)
stage 2 -1.549* -1.333 4.212*** -1.333 0.068 -3.362**
(0.873) (1.414) (1.579) (1.414) (1.581) (1.543)
contradiction x stage 2 3.721*** 5.546*** -0.192 5.848***
(1.221) (2.120) (2.054) (2.176)
both x stage 2 -2.029 -1.726
(2.093) (2.201)
interval x stage 2 1.401 -4.336**
(2.121) (2.052)
Constant 55.130*** 55.414*** 52.728*** 55.414*** 54.056*** 55.893***
(0.736) (1.200) (1.264) (1.200) (1.357) (1.273)
Observations 3,010 1,490 1,520 1,014 1,002 994
R2 0.006 0.002 0.010 0.005 0.009 0.013
Adjusted R2 0.005 -0.001 0.007 0.002 0.006 0.010
Residual Std. Error 21.788 22.070 21.473 21.291 21.762 22.259
F Statistic 5.977*** 0.717 3.041*** 1.812 3.054** 4.266***
Note: p<0.1; p<0.05; p<0.01
The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)

:::

5.7 Table B.6

::: {#tbl-B-6 .cell tbl-cap=’ ’}

ols_1 <- lm(formula = E23 ~ surprise + treated + surprise * treated,
              data = data)
  se_1  <- coeftest(x = ols_1, 
                    vcov = vcovCL(ols_1,
                                  cluster = ~data$participant.label,
                                  type = "HC1"))
  
  ols_2 <- lm(formula = E23 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == FALSE))
  se_2  <- coeftest(x = ols_2, 
                    vcov = vcovCL(ols_2,
                                  cluster = data[surprise == FALSE, participant.label],
                                  type = "HC1"))
  
  ols_3 <- lm(formula = E23 ~ communication + treated + communication * treated, 
              data = data,
              subset = (surprise == TRUE))
  se_3  <- coeftest(x = ols_3, 
                    vcov = vcovCL(ols_3,
                                  cluster = data[surprise == TRUE, participant.label],
                                  type = "HC1"))
  
  ols_4 <- lm(formula = E23 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "point"))
  se_4  <- coeftest(x = ols_4, 
                    vcov = vcovCL(ols_4,
                                  cluster = data[communication == "point", participant.label],
                                  type = "HC1"))
  
  ols_5 <- lm(formula = E23 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "interval"))
  se_5  <- coeftest(x = ols_5, 
                    vcov = vcovCL(ols_5,
                                  cluster = data[communication == "interval", participant.label],
                                  type = "HC1"))
  
  ols_6 <- lm(formula = E23 ~ surprise + treated + surprise * treated, 
              data = data,
              subset = (communication == "both"))
  se_6  <- coeftest(x = ols_6, 
                    vcov = vcovCL(ols_6,
                                  cluster = data[communication == "both", participant.label],
                                  type = "HC1"))
  
  
  
  se <- list(se_1[,2], se_2[,2], se_3[,2], se_4[,2], se_5[,2], se_6[,2])
  p  <- list(se_1[,4], se_2[,4], se_3[,4], se_4[,4], se_5[,4], se_6[,4])
  
  stargazer(ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, 
            align = TRUE, 
            se = se, 
            p = p,   
            title = "Linear regressions: Treatment effects on E23",
            dep.var.caption = "Dependent variable: E23",
            dep.var.labels = " ",
            model.names = FALSE,
            column.labels = c("full", "confirmation", "contradiction", "point", "interval", "both"),
            covariate.labels = c("contradiction", "both", "interval", "stage 2", "contradiction x stage 2", "both x stage 2", "interval x stage 2", "Constant"),
            font.size = "scriptsize",
            type = "html", 
            df = FALSE,
          notes = c("The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)"),
          notes.align = "l")
Linear regressions: Treatment effects on E23
Dependent variable: E23
full confirmation contradiction point interval both
(1) (2) (3) (4) (5) (6)
contradiction 1.513 0.254 1.193 3.086
(1.154) (2.075) (1.963) (1.959)
both 0.306 3.139
(2.028) (2.006)
interval 0.722 1.661
(2.047) (1.992)
stage 2 3.099*** 3.308** -7.562*** 3.308** 2.074 3.893**
(0.855) (1.389) (1.812) (1.389) (1.458) (1.597)
contradiction x stage 2 -10.200*** -10.869*** -7.545*** -12.211***
(1.326) (2.283) (2.198) (2.417)
both x stage 2 0.585 -0.756
(2.116) (2.564)
interval x stage 2 -1.234 2.091
(2.013) (2.447)
Constant 59.658*** 59.322*** 59.575*** 59.322*** 60.043*** 59.628***
(0.829) (1.452) (1.481) (1.453) (1.442) (1.416)
Observations 3,010 1,490 1,520 1,014 1,002 994
R2 0.020 0.005 0.027 0.026 0.012 0.024
Adjusted R2 0.019 0.001 0.023 0.023 0.009 0.021
Residual Std. Error 23.195 23.236 23.167 23.966 22.547 23.058
F Statistic 20.085*** 1.441 8.284*** 8.939*** 3.966*** 8.016***
Note: p<0.1; p<0.05; p<0.01
The underlying standard errors (“HC1”, in parentheses) are clustered at the individual level and estimated with the R package sandwich (Zeileis 2004; Zeileis et al. 2020)

:::

Session Info

sessionInfo()
R version 4.4.1 (2024-06-14)
Platform: x86_64-apple-darwin20
Running under: macOS Sonoma 14.4.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: Europe/Zurich
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] stargazer_5.2.3   sandwich_3.1-0    lmtest_0.9-40     zoo_1.8-12       
 [5] ggplot2_3.5.1     Rmisc_1.5.1       plyr_1.8.9        lattice_0.22-6   
 [9] stringr_1.5.1     data.table_1.15.4 magrittr_2.0.3   

loaded via a namespace (and not attached):
 [1] gtable_0.3.5      jsonlite_1.8.8    dplyr_1.1.4       compiler_4.4.1   
 [5] tidyselect_1.2.1  Rcpp_1.0.13       parallel_4.4.1    scales_1.3.0     
 [9] yaml_2.3.10       fastmap_1.2.0     R6_2.5.1          generics_0.1.3   
[13] knitr_1.48        htmlwidgets_1.6.4 tibble_3.2.1      munsell_0.5.1    
[17] pillar_1.9.0      rlang_1.1.4       utf8_1.2.4        stringi_1.8.4    
[21] xfun_0.46         cli_3.6.3         withr_3.0.1       digest_0.6.36    
[25] grid_4.4.1        rstudioapi_0.16.0 lifecycle_1.0.4   vctrs_0.6.5      
[29] evaluate_0.24.0   glue_1.7.0        groundhog_3.2.0   fansi_1.0.6      
[33] colorspace_2.1-1  rmarkdown_2.27    tools_4.4.1       pkgconfig_2.0.3  
[37] htmltools_0.5.8.1